// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "sparse.h"
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
#include <sstream>

template<typename Solver, typename Rhs, typename Guess, typename Result>
void
solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result& x)
{
	if (internal::random<bool>()) {
		// With a temporary through evaluator<SolveWithGuess>
		x = solver.derived().solveWithGuess(b, g) + Result::Zero(x.rows(), x.cols());
	} else {
		// direct evaluation within x through Assignment<Result,SolveWithGuess>
		x = solver.derived().solveWithGuess(b.derived(), g);
	}
}

template<typename Solver, typename Rhs, typename Guess, typename Result>
void
solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess&, Result& x)
{
	if (internal::random<bool>())
		x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols());
	else
		x = solver.derived().solve(b);
}

template<typename Solver, typename Rhs, typename Guess, typename Result>
void
solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess&, Result& x)
{
	x = solver.derived().solve(b);
}

template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
void
check_sparse_solving(Solver& solver,
					 const typename Solver::MatrixType& A,
					 const Rhs& b,
					 const DenseMat& dA,
					 const DenseRhs& db)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef typename Mat::StorageIndex StorageIndex;

	DenseRhs refX = dA.householderQr().solve(db);
	{
		Rhs x(A.cols(), b.cols());
		Rhs oldb = b;

		solver.compute(A);
		if (solver.info() != Success) {
			std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
			VERIFY(solver.info() == Success);
		}
		x = solver.solve(b);
		if (solver.info() != Success) {
			std::cerr << "WARNING: sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
			// dump call stack:
			g_test_level++;
			VERIFY(solver.info() == Success);
			g_test_level--;
			return;
		}
		VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x.isApprox(refX, test_precision<Scalar>()));

		x.setZero();
		solve_with_guess(solver, b, x, x);
		VERIFY(solver.info() == Success && "solving failed when using solve_with_guess API");
		VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x.isApprox(refX, test_precision<Scalar>()));

		x.setZero();
		// test the analyze/factorize API
		solver.analyzePattern(A);
		solver.factorize(A);
		VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
		x = solver.solve(b);
		VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
		VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x.isApprox(refX, test_precision<Scalar>()));

		x.setZero();
		// test with Map
		MappedSparseMatrix<Scalar, Mat::Options, StorageIndex> Am(A.rows(),
																  A.cols(),
																  A.nonZeros(),
																  const_cast<StorageIndex*>(A.outerIndexPtr()),
																  const_cast<StorageIndex*>(A.innerIndexPtr()),
																  const_cast<Scalar*>(A.valuePtr()));
		solver.compute(Am);
		VERIFY(solver.info() == Success && "factorization failed when using Map");
		DenseRhs dx(refX);
		dx.setZero();
		Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
		Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
		xm = solver.solve(bm);
		VERIFY(solver.info() == Success && "solving failed when using Map");
		VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(xm.isApprox(refX, test_precision<Scalar>()));
	}

	// if not too large, do some extra check:
	if (A.rows() < 2000) {
		// test initialization ctor
		{
			Rhs x(b.rows(), b.cols());
			Solver solver2(A);
			VERIFY(solver2.info() == Success);
			x = solver2.solve(b);
			VERIFY(x.isApprox(refX, test_precision<Scalar>()));
		}

		// test dense Block as the result and rhs:
		{
			DenseRhs x(refX.rows(), refX.cols());
			DenseRhs oldb(db);
			x.setZero();
			x.block(0, 0, x.rows(), x.cols()) = solver.solve(db.block(0, 0, db.rows(), db.cols()));
			VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!");
			VERIFY(x.isApprox(refX, test_precision<Scalar>()));
		}

		// test uncompressed inputs
		{
			Mat A2 = A;
			A2.reserve((ArrayXf::Random(A.outerSize()) + 2).template cast<typename Mat::StorageIndex>().eval());
			solver.compute(A2);
			Rhs x = solver.solve(b);
			VERIFY(x.isApprox(refX, test_precision<Scalar>()));
		}

		// test expression as input
		{
			solver.compute(0.5 * (A + A));
			Rhs x = solver.solve(b);
			VERIFY(x.isApprox(refX, test_precision<Scalar>()));

			Solver solver2(0.5 * (A + A));
			Rhs x2 = solver2.solve(b);
			VERIFY(x2.isApprox(refX, test_precision<Scalar>()));
		}
	}
}

// specialization of generic check_sparse_solving for SuperLU in order to also test adjoint and transpose solves
template<typename Scalar, typename Rhs, typename DenseMat, typename DenseRhs>
void
check_sparse_solving(Eigen::SparseLU<Eigen::SparseMatrix<Scalar>>& solver,
					 const typename Eigen::SparseMatrix<Scalar>& A,
					 const Rhs& b,
					 const DenseMat& dA,
					 const DenseRhs& db)
{
	typedef typename Eigen::SparseMatrix<Scalar> Mat;
	typedef typename Mat::StorageIndex StorageIndex;
	typedef typename Eigen::SparseLU<Eigen::SparseMatrix<Scalar>> Solver;

	// reference solutions computed by dense QR solver
	DenseRhs refX1 = dA.householderQr().solve(db);			   // solution of A x = db
	DenseRhs refX2 = dA.transpose().householderQr().solve(db); // solution of A^T * x = db (use transposed matrix A^T)
	DenseRhs refX3 = dA.adjoint().householderQr().solve(db);   // solution of A^* * x = db (use adjoint matrix A^*)

	{
		Rhs x1(A.cols(), b.cols());
		Rhs x2(A.cols(), b.cols());
		Rhs x3(A.cols(), b.cols());
		Rhs oldb = b;

		solver.compute(A);
		if (solver.info() != Success) {
			std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
			VERIFY(solver.info() == Success);
		}
		x1 = solver.solve(b);
		if (solver.info() != Success) {
			std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
			return;
		}
		VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));

		// test solve with transposed
		x2 = solver.transpose().solve(b);
		VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x2.isApprox(refX2, test_precision<Scalar>()));

		// test solve with adjoint
		// solver.template _solve_impl_transposed<true>(b, x3);
		x3 = solver.adjoint().solve(b);
		VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x3.isApprox(refX3, test_precision<Scalar>()));

		x1.setZero();
		solve_with_guess(solver, b, x1, x1);
		VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
		VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));

		x1.setZero();
		x2.setZero();
		x3.setZero();
		// test the analyze/factorize API
		solver.analyzePattern(A);
		solver.factorize(A);
		VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
		x1 = solver.solve(b);
		x2 = solver.transpose().solve(b);
		x3 = solver.adjoint().solve(b);

		VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
		VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));
		VERIFY(x2.isApprox(refX2, test_precision<Scalar>()));
		VERIFY(x3.isApprox(refX3, test_precision<Scalar>()));

		x1.setZero();
		// test with Map
		MappedSparseMatrix<Scalar, Mat::Options, StorageIndex> Am(A.rows(),
																  A.cols(),
																  A.nonZeros(),
																  const_cast<StorageIndex*>(A.outerIndexPtr()),
																  const_cast<StorageIndex*>(A.innerIndexPtr()),
																  const_cast<Scalar*>(A.valuePtr()));
		solver.compute(Am);
		VERIFY(solver.info() == Success && "factorization failed when using Map");
		DenseRhs dx(refX1);
		dx.setZero();
		Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
		Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
		xm = solver.solve(bm);
		VERIFY(solver.info() == Success && "solving failed when using Map");
		VERIFY(oldb.isApprox(bm, 0.0) && "sparse solver testing: the rhs should not be modified!");
		VERIFY(xm.isApprox(refX1, test_precision<Scalar>()));
	}

	// if not too large, do some extra check:
	if (A.rows() < 2000) {
		// test initialization ctor
		{
			Rhs x(b.rows(), b.cols());
			Solver solver2(A);
			VERIFY(solver2.info() == Success);
			x = solver2.solve(b);
			VERIFY(x.isApprox(refX1, test_precision<Scalar>()));
		}

		// test dense Block as the result and rhs:
		{
			DenseRhs x(refX1.rows(), refX1.cols());
			DenseRhs oldb(db);
			x.setZero();
			x.block(0, 0, x.rows(), x.cols()) = solver.solve(db.block(0, 0, db.rows(), db.cols()));
			VERIFY(oldb.isApprox(db, 0.0) && "sparse solver testing: the rhs should not be modified!");
			VERIFY(x.isApprox(refX1, test_precision<Scalar>()));
		}

		// test uncompressed inputs
		{
			Mat A2 = A;
			A2.reserve((ArrayXf::Random(A.outerSize()) + 2).template cast<typename Mat::StorageIndex>().eval());
			solver.compute(A2);
			Rhs x = solver.solve(b);
			VERIFY(x.isApprox(refX1, test_precision<Scalar>()));
		}

		// test expression as input
		{
			solver.compute(0.5 * (A + A));
			Rhs x = solver.solve(b);
			VERIFY(x.isApprox(refX1, test_precision<Scalar>()));

			Solver solver2(0.5 * (A + A));
			Rhs x2 = solver2.solve(b);
			VERIFY(x2.isApprox(refX1, test_precision<Scalar>()));
		}
	}
}

template<typename Solver, typename Rhs>
void
check_sparse_solving_real_cases(Solver& solver,
								const typename Solver::MatrixType& A,
								const Rhs& b,
								const typename Solver::MatrixType& fullA,
								const Rhs& refX)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef typename Mat::RealScalar RealScalar;

	Rhs x(A.cols(), b.cols());

	solver.compute(A);
	if (solver.info() != Success) {
		std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
		VERIFY(solver.info() == Success);
	}
	x = solver.solve(b);

	if (solver.info() != Success) {
		std::cerr << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
		return;
	}

	RealScalar res_error = (fullA * x - b).norm() / b.norm();
	VERIFY((res_error <= test_precision<Scalar>()) && "sparse solver failed without noticing it");

	if (refX.size() != 0 && (refX - x).norm() / refX.norm() > test_precision<Scalar>()) {
		std::cerr << "WARNING | found solution is different from the provided reference one\n";
	}
}
template<typename Solver, typename DenseMat>
void
check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;

	solver.compute(A);
	if (solver.info() != Success) {
		std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\n";
		return;
	}

	Scalar refDet = dA.determinant();
	VERIFY_IS_APPROX(refDet, solver.determinant());
}
template<typename Solver, typename DenseMat>
void
check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
{
	using std::abs;
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;

	solver.compute(A);
	if (solver.info() != Success) {
		std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
		return;
	}

	Scalar refDet = abs(dA.determinant());
	VERIFY_IS_APPROX(refDet, solver.absDeterminant());
}

template<typename Solver, typename DenseMat>
int
generate_sparse_spd_problem(Solver&,
							typename Solver::MatrixType& A,
							typename Solver::MatrixType& halfA,
							DenseMat& dA,
							int maxSize = 300)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;

	int size = internal::random<int>(1, maxSize);
	double density = (std::max)(8. / (size * size), 0.01);

	Mat M(size, size);
	DenseMatrix dM(size, size);

	initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);

	A = M * M.adjoint();
	dA = dM * dM.adjoint();

	halfA.resize(size, size);
	if (Solver::UpLo == (Lower | Upper))
		halfA = A;
	else
		halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);

	return size;
}

#ifdef TEST_REAL_CASES
template<typename Scalar>
inline std::string
get_matrixfolder()
{
	std::string mat_folder = TEST_REAL_CASES;
	if (internal::is_same<Scalar, std::complex<float>>::value || internal::is_same<Scalar, std::complex<double>>::value)
		mat_folder = mat_folder + static_cast<std::string>("/complex/");
	else
		mat_folder = mat_folder + static_cast<std::string>("/real/");
	return mat_folder;
}
std::string
sym_to_string(int sym)
{
	if (sym == Symmetric)
		return "Symmetric ";
	if (sym == SPD)
		return "SPD ";
	return "";
}
template<typename Derived>
std::string
solver_stats(const IterativeSolverBase<Derived>& solver)
{
	std::stringstream ss;
	ss << solver.iterations() << " iters, error: " << solver.error();
	return ss.str();
}
template<typename Derived>
std::string
solver_stats(const SparseSolverBase<Derived>& /*solver*/)
{
	return "";
}
#endif

template<typename Solver>
void
check_sparse_spd_solving(Solver& solver,
						 int maxSize = (std::min)(300, EIGEN_TEST_MAX_SIZE),
						 int maxRealWorldSize = 100000)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef typename Mat::StorageIndex StorageIndex;
	typedef SparseMatrix<Scalar, ColMajor, StorageIndex> SpMat;
	typedef SparseVector<Scalar, 0, StorageIndex> SpVec;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
	typedef Matrix<Scalar, Dynamic, 1> DenseVector;

	// generate the problem
	Mat A, halfA;
	DenseMatrix dA;
	for (int i = 0; i < g_repeat; i++) {
		int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);

		// generate the right hand sides
		int rhsCols = internal::random<int>(1, 16);
		double density = (std::max)(8. / (size * rhsCols), 0.1);
		SpMat B(size, rhsCols);
		DenseVector b = DenseVector::Random(size);
		DenseMatrix dB(size, rhsCols);
		initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
		SpVec c = B.col(0);
		DenseVector dc = dB.col(0);

		CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
		CALL_SUBTEST(check_sparse_solving(solver, halfA, b, dA, b));
		CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, halfA, dB, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, halfA, B, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc));
		CALL_SUBTEST(check_sparse_solving(solver, halfA, c, dA, dc));

		// check only once
		if (i == 0) {
			b = DenseVector::Zero(size);
			check_sparse_solving(solver, A, b, dA, b);
		}
	}

	// First, get the folder
#ifdef TEST_REAL_CASES
	// Test real problems with double precision only
	if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value) {
		std::string mat_folder = get_matrixfolder<Scalar>();
		MatrixMarketIterator<Scalar> it(mat_folder);
		for (; it; ++it) {
			if (it.sym() == SPD) {
				A = it.matrix();
				if (A.diagonal().size() <= maxRealWorldSize) {
					DenseVector b = it.rhs();
					DenseVector refX = it.refX();
					PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;
					halfA.resize(A.rows(), A.cols());
					if (Solver::UpLo == (Lower | Upper))
						halfA = A;
					else
						halfA.template selfadjointView<Solver::UpLo>() =
							A.template triangularView<Eigen::Lower>().twistedBy(pnull);

					std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
							  << " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..."
							  << std::endl;
					CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
					std::string stats = solver_stats(solver);
					if (stats.size() > 0)
						std::cout << "INFO |  " << stats << std::endl;
					CALL_SUBTEST(check_sparse_solving_real_cases(solver, halfA, b, A, refX));
				} else {
					std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
				}
			}
		}
	}
#else
	EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}

template<typename Solver>
void
check_sparse_spd_determinant(Solver& solver)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;

	// generate the problem
	Mat A, halfA;
	DenseMatrix dA;
	generate_sparse_spd_problem(solver, A, halfA, dA, 30);

	for (int i = 0; i < g_repeat; i++) {
		check_sparse_determinant(solver, A, dA);
		check_sparse_determinant(solver, halfA, dA);
	}
}

template<typename Solver, typename DenseMat>
Index
generate_sparse_square_problem(Solver&,
							   typename Solver::MatrixType& A,
							   DenseMat& dA,
							   int maxSize = 300,
							   int options = ForceNonZeroDiag)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;

	Index size = internal::random<int>(1, maxSize);
	double density = (std::max)(8. / (size * size), 0.01);

	A.resize(size, size);
	dA.resize(size, size);

	initSparse<Scalar>(density, dA, A, options);

	return size;
}

struct prune_column
{
	Index m_col;
	prune_column(Index col)
		: m_col(col)
	{
	}
	template<class Scalar>
	bool operator()(Index, Index col, const Scalar&) const
	{
		return col != m_col;
	}
};

template<typename Solver>
void
check_sparse_square_solving(Solver& solver,
							int maxSize = 300,
							int maxRealWorldSize = 100000,
							bool checkDeficient = false)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef SparseMatrix<Scalar, ColMajor, typename Mat::StorageIndex> SpMat;
	typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
	typedef Matrix<Scalar, Dynamic, 1> DenseVector;

	int rhsCols = internal::random<int>(1, 16);

	Mat A;
	DenseMatrix dA;
	for (int i = 0; i < g_repeat; i++) {
		Index size = generate_sparse_square_problem(solver, A, dA, maxSize);

		A.makeCompressed();
		DenseVector b = DenseVector::Random(size);
		DenseMatrix dB(size, rhsCols);
		SpMat B(size, rhsCols);
		double density = (std::max)(8. / (size * rhsCols), 0.1);
		initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
		B.makeCompressed();
		SpVec c = B.col(0);
		DenseVector dc = dB.col(0);
		CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
		CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB));
		CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc));

		// check only once
		if (i == 0) {
			CALL_SUBTEST(b = DenseVector::Zero(size); check_sparse_solving(solver, A, b, dA, b));
		}
		// regression test for Bug 792 (structurally rank deficient matrices):
		if (checkDeficient && size > 1) {
			Index col = internal::random<int>(0, int(size - 1));
			A.prune(prune_column(col));
			solver.compute(A);
			VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
		}
	}

	// First, get the folder
#ifdef TEST_REAL_CASES
	// Test real problems with double precision only
	if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value) {
		std::string mat_folder = get_matrixfolder<Scalar>();
		MatrixMarketIterator<Scalar> it(mat_folder);
		for (; it; ++it) {
			A = it.matrix();
			if (A.diagonal().size() <= maxRealWorldSize) {
				DenseVector b = it.rhs();
				DenseVector refX = it.refX();
				std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname() << " ("
						  << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
				CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
				std::string stats = solver_stats(solver);
				if (stats.size() > 0)
					std::cout << "INFO |  " << stats << std::endl;
			} else {
				std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
			}
		}
	}
#else
	EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}

template<typename Solver>
void
check_sparse_square_determinant(Solver& solver)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;

	for (int i = 0; i < g_repeat; i++) {
		// generate the problem
		Mat A;
		DenseMatrix dA;

		int size = internal::random<int>(1, 30);
		dA.setRandom(size, size);

		dA = (dA.array().abs() < 0.3).select(0, dA);
		dA.diagonal() = (dA.diagonal().array() == 0).select(1, dA.diagonal());
		A = dA.sparseView();
		A.makeCompressed();

		check_sparse_determinant(solver, A, dA);
	}
}

template<typename Solver>
void
check_sparse_square_abs_determinant(Solver& solver)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;

	for (int i = 0; i < g_repeat; i++) {
		// generate the problem
		Mat A;
		DenseMatrix dA;
		generate_sparse_square_problem(solver, A, dA, 30);
		A.makeCompressed();
		check_sparse_abs_determinant(solver, A, dA);
	}
}

template<typename Solver, typename DenseMat>
void
generate_sparse_leastsquare_problem(Solver&,
									typename Solver::MatrixType& A,
									DenseMat& dA,
									int maxSize = 300,
									int options = ForceNonZeroDiag)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;

	int rows = internal::random<int>(1, maxSize);
	int cols = internal::random<int>(1, rows);
	double density = (std::max)(8. / (rows * cols), 0.01);

	A.resize(rows, cols);
	dA.resize(rows, cols);

	initSparse<Scalar>(density, dA, A, options);
}

template<typename Solver>
void
check_sparse_leastsquare_solving(Solver& solver)
{
	typedef typename Solver::MatrixType Mat;
	typedef typename Mat::Scalar Scalar;
	typedef SparseMatrix<Scalar, ColMajor, typename Mat::StorageIndex> SpMat;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
	typedef Matrix<Scalar, Dynamic, 1> DenseVector;

	int rhsCols = internal::random<int>(1, 16);

	Mat A;
	DenseMatrix dA;
	for (int i = 0; i < g_repeat; i++) {
		generate_sparse_leastsquare_problem(solver, A, dA);

		A.makeCompressed();
		DenseVector b = DenseVector::Random(A.rows());
		DenseMatrix dB(A.rows(), rhsCols);
		SpMat B(A.rows(), rhsCols);
		double density = (std::max)(8. / (A.rows() * rhsCols), 0.1);
		initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
		B.makeCompressed();
		check_sparse_solving(solver, A, b, dA, b);
		check_sparse_solving(solver, A, dB, dA, dB);
		check_sparse_solving(solver, A, B, dA, dB);

		// check only once
		if (i == 0) {
			b = DenseVector::Zero(A.rows());
			check_sparse_solving(solver, A, b, dA, b);
		}
	}
}
